The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.
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April 1992
Research Papers
Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads
S. H. Choi
,
S. H. Choi
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125
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C. Pierre
,
C. Pierre
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125
Search for other works by this author on:
A. G. Ulsoy
A. G. Ulsoy
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125
Search for other works by this author on:
S. H. Choi
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125
C. Pierre
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125
A. G. Ulsoy
Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109-2125
J. Vib. Acoust. Apr 1992, 114(2): 249-259 (11 pages)
Published Online: April 1, 1992
Article history
Received:
November 1, 1990
Online:
June 17, 2008
Citation
Choi, S. H., Pierre, C., and Ulsoy, A. G. (April 1, 1992). "Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads." ASME. J. Vib. Acoust. April 1992; 114(2): 249–259. https://doi.org/10.1115/1.2930255
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